John Gabriel <email@example.com> wrote in news:firstname.lastname@example.org:
> On Wednesday, 26 February 2014 12:59:33 UTC+2, Wizard-Of-Oz wrote: > > > I am still waiting for you to give me even just ONE counterexample > which proves that (m+n) does not divide f(x+n)-f(x-m).
I never said you cannot divide f(x+n)-f(x-m) by (m+n). Unless m+n is zero, of course.
Every rational number can be divided by every non-zero rational number
Every real number can be divided by every non-zero real number
But YOU claimed it always divided *exactly*
To say a divides b exactly means the result of dividing b by a is an integer quotient (with a zero remainder). This is written a | b, and usually read as just "a divides b" (it is implicit that the result of the division is an integer) .. one doesn't even really need the addition of 'exactly'. a || b is sometimes used for "a exactly divides b" and is a more strict relationship. We don't need to go into that here.
>:-) Haaar, haaar. > > You can't because there isn't any.
Every answer for the division that is not an integer value is an counter example of your claim for exact division.